On our daily trips into Boston, we pass a lot of trucks on the highway, and a fair portion of them are designed for carrying liquids. I was struck by the variety of tank shapes, given that the regular dry containers all look basically the same. I assumed this had something to do with distributing the pressure such that the tank wouldn't rupture, and I decided to take a look at how the pressures would compare between three different designs: a cylindrical tube, a triangular tube, and a standard box. I chose the dimensions such that they all had the same width (they have to fit on the road after all) and all the same volume. The pressure exerted by standing water is given by
where
ρ is the density of water,
g the acceleration due to gravity, and
d the depth of the water. Applying this to each of the shapes, we find
where red is the highest pressure. We can get a more quantitative assessment of the shapes by finding the total force on the tank walls.
Evaluating this for each shape gives
| Circle |
|
| Triangle |
|
| Rectangle |
|
where
w is the width of the tanks. Throwing in some arbitrary values for our variables, we have
| Circle | 4 |
| Triangle | 3.14 |
| Rectangle | 5.6 |
suggesting that the triangular tube will have the least pressure. However, the triangle requires a much taller container to hold the same volume, so the circular tube offers a nice compromise.
That cylinder graph is neat. Circular shapes always seem to lead to unintuitive measurements.
ReplyDeleteHow about maximum pressure? It might be cheapest to manufacture the container out of a single material, rather than making some parts of it stronger than others.
I'm not an engineer, so I'm not too clear on the details of material strength, but if you were looking for smallest maximum pressure, you'd simply want the shortest container. In this case, that would be the rectangle, but I assume that's a bad idea, based on the fact that you don't see any on the road.
ReplyDeleteI was watching a passing train the other day, and I noticed that the "cylindrical" cars were actually slightly pinched toward the middle (of smaller radius about the same axis). Got any ideas why that might be a good design?
ReplyDeleteOff the top of my head, my guess would be for draining it. With a "flat" bottom, defects could trap the liquid, but by intentionally sloping it, that's much less likely.
ReplyDelete